Chapter 8: Internal Energy and the Laws of Thermodynamics

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1 Chapter 8: Internal Energy and the Laws of Thermodynamics Goals of Period 8 Section 8.1: To discuss conservation of energy and the first law of thermodynamics Section 8.: To discuss irreversible processes and perpetual motion Section 8.3: To describe the Ideal Gas Law Chapter 7 defined entropy as the measure of disorder of a system. It discussed the second law of thermodynamics, which relates entropy and equilibrium: a system is at its maximum entropy when that system is in equilibrium with its surroundings. Chapter 8 discusses the first law of thermodynamics, which is another way of looking at conservation of energy. Conservation of energy is applied to changes in the internal energy in a system. The change in the internal energy is equal to the heat added or subtracted from the system minus the work done by the system. 8.1 Conservation of Energy and the First Law of Thermodynamics Previously, when discussing friction, we did not deal with the motion of the molecules that produce thermal energy. When discussing a thermodynamic system we need to consider the motion of the molecules, which is the internal energy. We now restate conservation of energy to take into account internal energy. When energy is converted from one form into another form, the law of conservation of energy tells us that the total amount of energy does not change. Energy cannot be created or destroyed. When applied to thermodynamic systems, the law of conservation of energy is called the first law of thermodynamics. The first law of thermodynamics states that: change in internal energy of a system U equals the heat Q added to or subtracted from the system minus the work W done by the system, as shown in Equation 8.1. Conservation of energy is one reason why thermal equilibrium and thermodynamic systems are such important concepts. U = total internal energy (thermal energy) (joules) U = the change in internal energy (joules) Q U Q W (Equation 8.1) = heat added to or subtracted from the system (joules) W = work done by the system (joules) 65

2 8. Irreversible Processes We have seen that a system moving towards equilibrium is a system that has the ability to do work. As long as the system is not in equilibrium with its environment, the entropy it has compared to the entropy it will have when it reaches equilibrium is a measure of the amount of work that can be obtained from the system as it goes to equilibrium. To change a system from its equilibrium state requires that work be done on the system or that energy be added to the system or both. Any process is irreversible if, after a system has reached equilibrium, we cannot return the system to its original non-equilibrium situation without adding energy to it. A reversible process is one that could return the system to its original state without the addition of energy. Another way of stating the second law of thermodynamics is: All physical processes are irreversible. This is true for everything from the mixing of paint to the burning of fuel oil in electric power plants. Because all physical processes are irreversible, if one takes a series of pictures of a system as it progresses from a non-equilibrium to an equilibrium situation, then in many cases a person who did not observe the actual sequence of events can properly arrange the series of pictures on the basis of common experience. Since energy is conserved, why can't we simply run a process backward and return to the original situation? The answer is that in every process, part of the energy of the system is converted by friction into thermal energy. Frictional effects occur not only in mechanical systems, but also in chemical, electrical, magnetic and nuclear systems. The resulting thermal energy cannot be completely reconverted into other forms of energy. Heat will not flow from a cooler object to a warmer object unless energy is provided to cause the transfer. This is an example of an irreversible process. When energy is transferred to a system, some energy becomes thermal energy because of the molecules in the system. Regardless of how careful we are, we can never construct a device that is completely free from this energy conversion process. The production of thermal energy in this manner is ordinarily attributed to friction, and we speak of frictional losses when referring to the production of this thermal energy. Because all observable physical processes involve the interaction of material objects with each other or with radiation, all such physical processes are irreversible. The efficiency with which energy contained in any fuel is converted to a useful form varies widely, depending on the method of conversion and the end use desired. The efficiency of a device is equal to the amount of energy converted to the desired form divided by the amount of energy supplied to the device. All devices or processes result in some production of thermal energy, and this energy cannot be completely converted back into work. Therefore, the efficiency of a process is always less than one. 66

3 In theory, a perpetual motion machine is one that could run forever without input of energy. This implies the machine would produce no wasted energy and have an efficiency equal to one. Because some energy is wasted when energy is transferred in a system, all designs for perpetual motion machines are unfortunately doomed to failure. All devices or processes result in some production of thermal energy, and this energy cannot be completely converted back into work. An example of a system that is close to reversible is a pendulum that has a support with almost no friction, moving in a vacuum. However, this system does produce some wasted thermal energy. The second law of thermodynamics can be stated as follows: The entropy of a physical system with no external changes will increase or, if the system is already at its maximum entropy, the entropy will remain the same. Any system, with no external changes tends toward equilibrium with its surroundings. The entropy of a system that is in equilibrium with its surroundings remains constant. All physical processes are irreversible. Energy input is required to return a system at equilibrium to its non-equilibrium state. 8.3 Pressure, Temperature, Volume and the Ideal Gas Law If energy is added to a substance in a solid or liquid state and if the substance remains in that state, the temperature of the substance will increase. The amount of energy required to increase the temperature of a unit of mass of a substance is obtained by measuring the specific heat of the substance. Specific heat varies substantially from material to material. In general, the specific heat of a material depends on the temperature of the material and on whether the material is in a solid, liquid, or gaseous state. Visually, we think of the states of matter in terms of their large-scale or macroscopic behavior solid, liquid, or gas. When studying the phases of matter at the microscopic or atomic level, the phases are quite different. We know that objects such as a chair or a TV set are held together by some attractive force between the molecules that make up the objects. If we were just looking at molecules flying around randomly, we would not see them as a block of iron or a chair. It is very good that molecules in an object attract each other because of the forces between the molecules. In solids the attractive forces are strong enough to keep the molecules close together, sometimes in very regular arrangements. In the liquid state, the attractive forces between the molecules are not as strong and the molecules move around each other. But for gasses, the high speed molecules do not stay close to each other. They move in a random 67

4 manner, and when the molecules do hit each other, the attractive forces are not large enough to keep them close together. This is why a gas in a closed container will fill the container. However, if you put a liquid or solid in a container, it will stay at the bottom of the container. As discussed in Chapter 5, the higher the average molecular speed in a material, the higher the temperature T. Experiments have shown that when the size of the container of gas is held fixed, the pressure P of the gas, which is the force per unit area that the gas exerts on the walls of its container, is proportional to the temperature of the gas. So, at a fixed volume, P We also know that if we increase the temperature of a gas but do not exert any force to hold the volume of its container fixed, the pressure will stay fixed and the volume of the gas will expand. Therefore, the volume V of the gas in a container is also proportional to the gas temperature. Thus, at fixed pressure, V These two experimental results can be combined into the single relationship shown in Equation 8.. T T P V T is a symbol indicating proportional to P = pressure the gas exerts (newtons/meters ) V = the volume of the gas (meters 3 ) T = temperature (Kelvin) (Equation 8.) Concept Check 8.1 a) Use ratio reasoning to determine how the pressure exerted by a gas would change if the temperature of the gas was doubled (and all other variables were held constant). b) Use ratio reasoning to determine how the pressure exerted by a gas would change if the volume of the gas was doubled (and all other variables were held constant). 68

5 The average speed of the gas molecules depends on both the temperature of the gas and the mass of the molecules. Figure 8.1 illustrates the average speed of two different gases at the same temperature. The oxygen gas molecules are more massive and move randomly with a lower average speed than the molecules of the less massive helium molecules. Figure 8.1 Comparison of Molecular Speeds of Two Gases Because the shape of these graphs is known, the average kinetic energy of a molecule of the gas can be calculated and is found to be directly proportional to the absolute temperature of the gas. Recall that kinetic energy can be expressed as (Equation 8.3) Experimentally, the average kinetic energy of a molecule of gas has been found to be 3/ kt. Therefore, (Equation 8.4) 1 3 M v avg k T E 1 M kin v avg M = mass of a gas molecule (kilograms) v avg = the average velocity of the molecules (meters/sec) k = Boltzmann s constant (1.38 x 10 3 J/K) T = temperature of the gas (Kelvin) The internal energy is the energy due to the random motion of the molecules inside the container, rather than any possible motion of the container as a whole. If there are N number of molecules of a gas in a container of volume V, then the total energy of the gas in the container (the total internal energy of the system) is 3/ N k T. By experiment, the pressure of the gas times the volume of the container equals /3 of the total energy, 3/ N k T. Therefore, we can replace the proportional relationship in Equation 8. by the equation 69

6 P V 3 3 N k T This results in the Ideal Gas Law as shown in Equation 8.5. P V N k T P = pressure the gas exerts (newtons/meters ) V = the volume of the gas (meters 3 ) N = the number of gas molecules k = Boltzmann s constant (1.38 x 10 3 J/K degree) T = temperature (Kelvin) (Equation 8.5) Using ratio reasoning, we see that Equation 8.5 seems very reasonable. If we keep the volume of a gas constant, increasing the number of molecules of gas in the volume or increasing the temperature of the gas would be expected to increase the pressure. Likewise, if you want to keep the pressure and temperature constant, increasing the volume of the gas would require increasing the number of molecules of the gas filling that volume. Period 8 Summary 8.1: Entropy is a measure of the degree of disorder of a system. The greater the disorder, the greater the amount of entropy. Entropy increase over time. The first law of thermodynamics: the change in internal energy of a system equals the heat added to the system minus the work done by the system. U = Q W 8.: As systems move toward equilibrium, they can give off energy or do work or do both. To change a system from its equilibrium state requires that work be done on the system or that energy be added to the system or both. Physical changes are irreversible if energy must be added or work be done or both to return the system to its original state. All physical processes are irreversible. The second law of thermodynamics can be stated in several ways: 1) The entropy of a physical system with no external changes will increase or, if the system is already at its maximum entropy, the entropy will remain the same. ) Any system with no external changes tends toward equilibrium with its surroundings. 3) The entropy of a system that is in equilibrium with its surroundings remains constant. 4) All physical processes are irreversible. They require energy input to move a system at equilibrium to non-equilibrium. 8.3: The ideal gas law describes the relationship among the pressure, temperature, and volume of a gas and number of molecules in a gas: P V = N k T 70

7 Solution to Chapter 8 Concept Check 8.1 a) Equation 8. shows that pressure and temperature are directly proportional. If you double the temperature of the gas, the pressure doubles also. b) Pressure and volume are inversely proportional. This may be seen more easily by solving Equation 8. for pressure. P N k T V Doubling the volume reduces the pressure to ½ of its original value. P N k T V 71

Preview of Period 7: Applications of the Laws of Thermodynamics

Preview of Period 7: Applications of the Laws of Thermodynamics 7.1 Conservation of Energy and the 1 st Law of Thermodynamics ow does conservation of energy relate to molecular motion? What is the 1 st